Many clients are stressed out by how their tattoo looks when its brand new and fresh. The area that has been tattooed is normally a bit swollen, red and very sore to the touch. Sometimes there is even bruising as well! This is all normal.
OBS:(If you have any stinging pain or strange colored liquid coming out of your tattoo thats different and might be signs of an infection. Im just describing the normal redness related directly to just having had a tattoo done. If your in doubt about your tattoo call your artist right away for some advice!)
As you can see in the photo the area around the tattoo can get very red during tattooing. This is absolutely normal and only natural considering the "beating" your skin takes when you get tattooed. A tattoo is an open wound and needs care to heal well. But while its healing, particularly the first couple of days, it might look a bit red and swollen like I mentioned already.
Also: black and gray tattoos look very dark the first week or so after they are first completed. The redness of the tattooed skin make the shading appear much, much darker than it really is! Let it heal before you judge it. It is going to take a couple of weeks for you to truly see all the shades properly the way they where intended; ranging from deepest black to softest gray! This is also an issue with color tattoos but I find it to be a bigger issue with black and gray. Give it a bit of time and good aftercare and enjoy the results!